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Congestion Games with Priority-Based Scheduling

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Algorithmic Game Theory (SAGT 2020)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 12283))

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Abstract

We reconsider atomic and non-atomic affine congestion games under the assumption that players are partitioned into p priority classes and resources schedule their users according to a priority-based policy, breaking ties uniformly at random. We derive tight bounds on both the price of anarchy and the price of stability as a function of p, revealing an interesting separation between the general case of \(p\ge 2\) and the priority-free scenario of \(p=1\). In fact, while non-atomic games are more efficient than atomic ones in absence of priorities, they share the same price of anarchy when \(p\ge 2\). Moreover, while the price of stability is lower than the price of anarchy in atomic games with no priorities, the two metrics become equal when \(p\ge 2\). Our results hold even under singleton strategies. Besides being of independent interest, priority-based scheduling shares tight connections with online load balancing and finds a natural application within the theory of coordination mechanisms and cost-sharing policies for congestion games. Under this perspective, a number of possible research directions also arises.

This work was partially supported by the Italian MIUR PRIN 2017 Project ALGADIMAR “Algorithms, Games, and Digital Markets”.

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References

  1. Aland, S., Dumrauf, D., Gairing, M., Monien, B., Schoppmann, F.: Exact price of anarchy for polynomial congestion games. SIAM J. Comput. 40(5), 1211–1233 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  2. Anshelevich, E., Dasgupta, A., Kleinberg, J., Tardos, E., Wexler, T., Roughgarden, T.: The price of stability for network design with fair cost allocation. SIAM J. Comput. 38(4), 1602–1623 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  3. Awerbuch, B., Azar, Y., Epstein, L.: The price of routing unsplittable flow. In Proceedings of STOC, pp. 57–66. ACM (2005)

    Google Scholar 

  4. Beckmann, M., McGuire, C.B., Winsten, C.B.: Studies in the economics of transportation. Yale University Press, New Haven (1956)

    Google Scholar 

  5. Bhawalkar, K., Gairing, M., Roughgarden, T.: Weighted congestion games: price of anarchy, universal worst-case examples, and tightness. ACM Trans. Econ. Comp. 2(4), 1–23 (2014)

    Article  MATH  Google Scholar 

  6. Bilò, V.: On the robustness of the approximate price of anarchy in generalized congestion games. In: Gairing, M., Savani, R. (eds.) SAGT 2016. LNCS, vol. 9928, pp. 93–104. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53354-3_8

    Chapter  Google Scholar 

  7. Bilò, V.: A unifying tool for bounding the quality of non-cooperative solutions in weighted congestion games. Theor. Comput. Syst. 62(5), 1288–1317 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  8. Bilò, V., Fanelli, A., Flammini, M., Moscardelli, L.: Performances of one-round walks in linear congestion games. Theor. Comput. Syst. 49(1), 24–45 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  9. Bilò, V., Vinci, C.: On the impact of singleton strategies in congestion games. In: Proceedings of ESA, of LIPIcs, vol. 87, pp. 17:1–17:14. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik (2017)

    Google Scholar 

  10. Bilò, V., Vinci, C.: The price of anarchy of affine congestion games with similar strategies. Theor. Comput. Sci. 806, 641–654 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  11. Bilò, V., Moscardelli, L., Vinci, C.: Uniform mixed equilibria in network congestion games with link failures. In: Proceedings of ICALP, of LIPIcs, vol. 107, pp. 146:1–146:14. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik (2018)

    Google Scholar 

  12. Caragiannis, I.: Better bounds for online load balancing on unrelated machines. In: Proceedings of SODA, pp. 972–981. ACM (2008)

    Google Scholar 

  13. Caragiannis, I., Flammini, M., Kaklamanis, C., Kanellopoulos, P., Moscardelli, L.: Tight bounds for selfish and greedy load balancing. Algorithmica 61(3), 606–637 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  14. Caragiannis, I., Gkatzelis, V., Vinci, C.: Coordination mechanisms, cost-sharing, and approximation algorithms for scheduling. In: Devanur, N.R., Lu, P. (eds.) WINE 2017. LNCS, vol. 10660, pp. 74–87. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-71924-5_6

    Chapter  MATH  Google Scholar 

  15. Christodoulou, G., Gairing, M.: Price of stability in polynomial congestion games. ACM Trans. Econ. Comp. 42(2), 101–1017 (2016)

    MathSciNet  MATH  Google Scholar 

  16. Christodoulou, G., Gairing, M., Giannakopoulos, Y., Spirakis, P.G.: The price of stability of weighted congestion games. SIAM J. Comput. 48(5), 1544–1582 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  17. Christodoulou, G., Koutsoupias, E.: On the price of anarchy and stability of correlated equilibria of linear congestion games. In: Brodal, G.S., Leonardi, S. (eds.) ESA 2005. LNCS, vol. 3669, pp. 59–70. Springer, Heidelberg (2005). https://doi.org/10.1007/11561071_8

    Chapter  Google Scholar 

  18. Christodoulou, G., Koutsoupias, E.: The price of anarchy of finite congestion games. In: Proceedings of STOC, pp. 67–73. ACM (2005)

    Google Scholar 

  19. Christodoulou, G., Koutsoupias, E., Nanavati, A.: Coordination mechanisms. Theor. Comput. Sci. 410(36), 3327–3336 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  20. Christodoulou, G., Koutsoupias, E., Spirakis, P.G.: On the performance of approximate equilibria in congestion games. Algorithmica 61(1), 116–140 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  21. Christodoulou, G., Mirrokni, V.S., Sidiropoulos, A.: Convergence and approximation in potential games. Theor. Comput. Sci. 438, 13–27 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  22. Cole, R., Correa, J.R., Gkatzelis, V., Mirrokni, V.S., Olver, N.: Inner product spaces for minsum coordination mechanisms. In: Proceedings of STOC, pp. 539–548. ACM (2011)

    Google Scholar 

  23. Cominetti, R., Scarsini, M., Schröder, M., Stier-Moses, N.E.: Price of anarchy in stochastic atomic congestion games with affine costs. In: Proceedings of EC, pp. 579–580. ACM (2019)

    Google Scholar 

  24. Correa, J.R., Cristi, A., Oosterwijk, T.: On the price of anarchy for flows over time. In: Proceedings of EC, pp. 559–577. ACM (2019)

    Google Scholar 

  25. Correa, J.R., Schulz, A.S., Stier-Moses, N.E.: Selfish routing in capacitated networks. Math. Oper. Res. 29(4), 961–976 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  26. Dafermos, S.C., Sparrow, F.T.: The traffic assignment problem for a general network. J. Res. Natl. Bureau Stand. 73B(2), 91–118 (1969)

    Article  MathSciNet  MATH  Google Scholar 

  27. de Jong, J., Kern, W., Steenhuisen, B., Uetz, M.: The asymptotic price of anarchy for k-uniform congestion games. In: Solis-Oba, R., Fleischer, R. (eds.) WAOA 2017. LNCS, vol. 10787, pp. 317–328. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-89441-6_23

    Chapter  Google Scholar 

  28. Farzad, B., Olver, N., Vetta, A.: A priority-based model of routing. Chicago J. Theor. Comput. Sci., 28 (2008)

    Google Scholar 

  29. Feldman, M., Immorlica, N., Lucier, B., Roughgarden, T., Syrgkanis, V.: The price of anarchy in large games. In: Proceedings of STOC, pp. 963–976. ACM (2016)

    Google Scholar 

  30. Gairing, M., Lücking, T., Mavronicolas, M., Monien, B.: The price of anarchy for polynomial social cost. Theor. Comput. Sci. 369(1–3), 116–135 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  31. Gairing, M., Schoppmann, F.: Total latency in singleton congestion games. In: Deng, X., Graham, F.C. (eds.) WINE 2007. LNCS, vol. 4858, pp. 381–387. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-77105-0_42

    Chapter  Google Scholar 

  32. Gkatzelis, V., Kollias, K., Roughgarden, T.: Optimal cost-sharing in general resource selection games. Oper. Res. 64(6), 1230–1238 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  33. Gopalakrishnan, R., Marden, J.R., Wierman, A.: Potential games are necessary to ensure pure nash equilibria in cost sharing games. Math. Oper. Res. 39(4), 1252–1296 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  34. Ieong, S., McGrew, R., Nudelman, E., Shoham, Y., Sun, Q.: Fast and compact: a simple class of congestion games. In: Proceedings of the 20th National Conference on Artificial Intelligence, AAAI, pp. 489–494. AAAI Press (2005)

    Google Scholar 

  35. Klimm, M., Schmand, D., Tönnis, A.: The online best reply algorithm for resource allocation problems. In: Fotakis, D., Markakis, E. (eds.) SAGT 2019. LNCS, vol. 11801, pp. 200–215. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-30473-7_14

    Chapter  Google Scholar 

  36. Koutsoupias, E., Papadimitriou, C.: Worst-case equilibria. In: Meinel, C., Tison, S. (eds.) STACS 1999. LNCS, vol. 1563, pp. 404–413. Springer, Heidelberg (1999). https://doi.org/10.1007/3-540-49116-3_38

    Chapter  Google Scholar 

  37. Lücking, T., Mavronicolas, M., Monien, B., Rode, M.: A new model for selfish routing. Theor. Comput. Sci. 406(3), 187–2006 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  38. Nash, J.F.: Equilibrium points in \(n\)-person games. Proc. Natl. Acad. Sci. 36(1), 48–49 (1950)

    MathSciNet  MATH  Google Scholar 

  39. Piliouras, G., Nikolova, E., Shamma, J.S.: Risk sensitivity of price of anarchy under uncertainty. ACM Trans. Econ. Comp. 5(1), 51–527 (2016)

    MathSciNet  Google Scholar 

  40. Rosenthal, R.W.: A class of games possessing pure-strategy nash equilibria. Int. J. Game Theory 2(1), 65–67 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  41. Roughgarden, T.: The price of anarchy is independent of the network topology. J. Comput. System Sci. 67(2), 341–364 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  42. Roughgarden, T.: Intrinsic robustness of the price of anarchy. J. ACM 62(5), 321–3242 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  43. Roughgarden, T., Tardos, E.: How bad is selfish routing? J. ACM 49(2), 236–259 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  44. Suri, S., Tóth, C., Zhou, Y.: Selfish load balancing and atomic congestion games. Algorithmica 47(1), 79–96 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  45. Vinci, C.: Non-atomic one-round walks in congestion games. Theor. Comput. Sci. 764, 61–79 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  46. von Falkenhausen, P., Harks, T.: Optimal cost sharing for resource selection games. Math. Oper. Res. 38(1), 184–208 (2013)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics and Physics, University of Salento, Lecce, Italy

    Vittorio Bilò

  2. Department of Computer Science, Gran Sasso Science Institute, L’Aquila, Italy

    Cosimo Vinci

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  1. Vittorio Bilò
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  2. Cosimo Vinci
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Correspondence to Vittorio Bilò .

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Editors and Affiliations

  1. Institute of Mathematics, Augsburg University, Augsburg, Germany

    Tobias Harks

  2. Institute of Mathematics, Technical University Berlin, Berlin, Germany

    Max Klimm

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Bilò, V., Vinci, C. (2020). Congestion Games with Priority-Based Scheduling. In: Harks, T., Klimm, M. (eds) Algorithmic Game Theory. SAGT 2020. Lecture Notes in Computer Science(), vol 12283. Springer, Cham. https://doi.org/10.1007/978-3-030-57980-7_5

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  • DOI: https://doi.org/10.1007/978-3-030-57980-7_5

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